Chapter 11.11 homework: Taylor and Maclaurin series Applications
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Review problems (not optional, but the usual even/odd policy applies)
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Question A:
i) An Amtrak train is currently (time=0) at position 0,
going 20 meters/sec, accelerating at 3 m/s^2.
What will its position be
after 2 seconds?
ii) A train is going 15 meters/sec, accelerating at 3 m/s^2.
How far will
it go in 2 seconds?
iii) A train is currently (time=0) at position 0,
going 5 meters/sec, accelerating at 1.5 m/s^2, with a jerk of 0.55 m/s^3
and a snap of 0.01 m/s^4.
What will its position be after 2 seconds?
iv) Consider that same train from part (iii).
What is its velocity at t=2?
v) Consider that same train from part (iii).
What is its acceleration at t=2?
Question B:
i) If you do a firstorder Taylor approximation to sin(x) at x=pi/4,
will your results be an upper bound or lower bound (or neither) on sin(x) for
values of x close to pi/4 ?
ii) If you do a 2ndorder Maclaurin approximation to cos(x),
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 '08
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 Derivative, Maclaurin Series, Taylor Series, Rate equation, Maclaurin series Applications

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